SSAT Middle Level Quantitative - How to find the area of a rectangle

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

Explanation

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is $4 \times 1 = 4$ , and its area is $1^{2} = 1$ .

The perimeter of the first square is $\frac{7}{4} \times 4 = 7$ , and its sidelength is $7 \div 4 = \frac{7}{4}$ . The area of this square is therefore $\left (\frac{7}{4} \right )^{2} =\frac{49}{16}$ .

The ratio of the areas is therefore $\frac{49}{16} : 1 = 49:16$ .

Rectangle

Give the area of the above rectangle in square feet.

$216 \textrm{ ft}^{2}$

$532\textrm{ ft}^{2}$

$576 \textrm{ ft}^{2}$

$33 \textrm{ ft}^{2}$

$66 \textrm{ ft}^{2}$

Explanation

Since 1 yard = 3 feet, multiply each dimension by 3 to convert from yards to feet:

$8 \textrm{ yd} \times 3 \textrm{ ft/yd} = 24 \textrm{ ft}$

$3 \textrm{ yd} \times 3 \textrm{ ft/yd} = 9 \textrm{ ft}$

Use the area formula, substituting :

$A = 24 \times 9 = 216$ square feet

Order the following from least area to greatest area:

Figure A: A rectangle with length 10 inches and width 14 inches.

Figure B: A square with side length 1 foot.

Figure C: A triangle with base 16 inches and height 20 inches.

Explanation

Figure A has area $10 \times 14 = 140$ square inches.

Figure B has area $12 \times 12 = 144$ square inches, 1 foot being equal to 12 inches.

Figure C has area $\frac{1}{2} \times 16 \times 20 = 160$ square inches.

The figures, arranged from least area to greatest, are A, B, C.

Which of the following is the area of a rectangle with a width of 4 feet and a length that is twice the width?

$32\ \text{ft}^2$

$34\ \text{ft}^2$

$36\ \text{ft}^2$

$16\ \text{ft}^2$

$64\ \text{ft}^2$

Explanation

The area of a rectangle is found by multiplying the width by the length.

$A=w\times l$

We know that the width is 4 feet and the the length must be twice the width. Multiply the width by 2 to find the length.

$l=2\times w$

$l=2\times4=8$

Multiply the length and width to find the area.

$4\times8=32$

The following question is about the Jones family wanting to buy square foot tiles for their rectangular basement. Their basement perimeter is 74 feet, with one of the sides being 15 feet long.

How many square foot titles are the Jones family needing to purchase in order to tile their basement?

Explanation

From the given information we know that the perimeter of the rectangular basement is 74 feet. We also know that one side of the rectangular basement is 15 feet. This means that the opposite side is also 15 feet long because the equivalent opposite sides rule of rectangles. In order to find the lengths of our other two sides of the rectangle, we need to subtract our two 15 feet sides from the perimeters 74 feet.

$74-30=44\ feet$ .

We know that the last two sides have to add up to 44 feet. Since the rules of rectangles say opposite sides are equivalent, we must take 44 feet and divide by the 2 sides. So 44 divided by 2 is 22 feet, meaning each side must be 22 feet. After adding up all the sides we can confirm that our perimeter is 74 feet.

Now we know all the sides of the rectangle, we are able to move to the next step, finding the area. We must find the area, because the tiles are square feet. So in order to find the area we must take the length of the rectangle and multiply it to the width.

$22\times 15= 330 ft^{2}$

Knowing the area of the rectangular basement we also know how many tile are needed to fill the basement for the Jones family. It is exactly 330 square feet tile needed.

A rectangular table has a length of $2.2\ m$ and a width of $1.5\ m$ . Give the area of the table.

$33000\ cm^2$

$3300\ cm^2$

$3000\ cm^2$

$30000\ cm^2$

$330\ cm^2$

Explanation

We know that:

$Area=a\times b$

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$Area=2.2\ m \times 1.5\ m=(2.2\times 100\ cm)\times (1.5\times 100\ cm)=33000\ cm^2$

If the length of a rectangle is 7.5 feet and the width is 2 feet, what is the value of if the area is ?

Explanation

The area of a rectangle is calculated by multiplying the length by the width. Here, the length is 7.5 and the width is 2, so the area will be 15.

Given that the area is also equal to , the value of will be 3, given that 3 times 5 is 15.

The rectangle above is inches long and inches wide. What is the area of the rectangle?

Note: Figure not drawn to scale.

$50: in^{2}$

$30: in^{2}$

Explanation

The area of the rectangle is $50: in^{2}$ . In order to find the area of a rectangle, multiply the length (5 inches) by the width (10 inches). The answer is in units2 because the area, by definition, is the number of square units that cover the inside of a figure.

Rectangles

Note: Figure NOT drawn to scale.

What percent of the above figure is red?

The correct answer is not given among the other choices.

$66 \frac{2}{3} %$

$87 \frac{1}{2} %$

Explanation

The large rectangle has length 80 and width 40, and, consequently, area

$80 \times 40 = 3,200$ .

The white region is a rectangle with length 30 and width 20, and, consequently, area

$30 \times 20 = 600$ .

The red region, therefore, has area .

The red region is

$\frac{2,600}{3,200} \times 100 = 81 \frac{1}{4} %$

of the large rectangle.

This is not one of the choices.

Rectangles 1

Refer to the above figures. The square at left has area 160. Give the area of the rectangle at right.

Explanation

The area of the square, whose sides have length , is the square of this sidelength, which is $x^{2}$ . The area of the rectangle is the product of the lengths of its sides; this is $2x \cdot \frac{1}{2} x = 2 \cdot \frac{1}{2} \cdot x \cdot x = x^{2}$

The square and the rectangle have the same area, so the correct response is 160.

How to find the area of a rectangle

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